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"Perilaku pasca elastik struktur jembatan akibat beban siklik gempa dapat ditunjukkan dengan melakukan analisa riwayat waktu nonlinear. Desain struktur berbasis kinerja (performance based design) diawali dengan pembentukan sendi plastis pada elemen nonlinear jembatan yang tergambar pada kurva momenrotasinya. Definisi potensi sendi plastis dinyatakan dengan penentuan panjang sendi plastis (lp) dan diskritisasi fiber section pada elemen nonlinear struktur (pilar jembatan). Penelitian ini bertujuan untuk melakukan studi parametrik panjang sendi plastis, bentuk penampang pilar, serta pemodelan pondasi terhadap kinerja struktur yang dihasilkan. Disamping itu juga dilakukan tinjauan sensitifitas spektrum gempa terhadap pembentukan sendi plastis. Penelitian ini diawali dengan melakukan pemodelan struktur jembatan, dimana pilar jembatan didesain ulang agar mengalami pelelehan pada saat gempa berlangsung. Hasil penelitian menunjukkan bahwa panjang sendi plastis yang ditempatkan pada pilar berbanding lurus dengan maksimum rotasi yang dihasilkan. Bentuk penampang pilar bulat terbukti memiliki kinerja yang lebih baik dibandingkan penampang persegi. Selain itu, pemodelan pondasi dalam desain struktur sebaiknya juga dilakukan untuk mendapatkan desain yang lebih konservatif. Dalam studi sensitifitas spektrum gempa, ditunjukkan bahwa respons struktur akan teramplifikasi pada saat frekuensi natural struktur berdekatan dengan muatan frekuensi dominan spektrum gempa.

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Structural post-elastic behavior due to earthquake cyclic loading can be shown by examining a nonlinear time history analysis. Structural design using the approach of performance based design is started with the forming of plastic hinges on the bridge nonlinear elements that is captured on its moment-rotation curves. The definition of potential plastic hinges is defined by the assignment of plastic hinge length (lp) and the discretization of fiber section on structure?s nonlinear elements (bridge piers).

The purpose of this research is to do a parametric study of plastic hinge length, piers cross section shape, and the foundation modeling to the obtained structural performance level. Besides that, this research will also review the sensitivity of earthquake spectrum to the forming of plastic hinges. This research is started with bridge structural modeling, where the piers will be redesigned so that their yielding limit exceeded when the earthquake happened.

The result of this research shows that the assignment of plastic hinge length is proportional to the obtained maximum rotation. Circular sections have a better performance compared to rectangular sections. Besides that, foundation modeling in structural design should be observed to get a more conservative design. In the sensitivity study of earthquake spectrum, this research shows that structural responses will be amplified when the frequency content of the motion and the natural frequencies of the structure are close to each other."

"Sistem rekomendasi (recommendation system) terus dikembangkan khususnya pada aplikasi teknik analisis data dalam membantu pengguna on-line (user) menemukan produk (item) yang ingin mereka beli. Satu dari beberapa metode dalam sistem rekomendasi adalah collaborative filtering (CF) dengan pendekatan latent variable models berdasarkan faktorisasi matriks. Hubungan antara pengguna (users) dan produk (item) dalam collaborative filtering dapat disajikan dalam bentuk matriks rating R. Penelitian ini membahas metode collaborative filtering berbasis model faktorisasi matriks pada sistem rekomendasi.Dalam faktorisasi matriks, permasalahan utamanya adalah mencari dua buah matriks Wm x k dan matriks Hk x m sehingga WH ≈ R dengan Rm x n. Akurasi dari model tercermin dari besarnya norm ║R-WH║ pada data testing. Terdapat beberapa teknik faktorisasi yang telah digunakan dalam CF. Dalam penelitian ini metode yang digunakan adalah faktorisasi matriks dengan metode gradient descent.Berdasarkan eksperimen, parameter model yang optimal yang memenuhi fungsi optimasi diperoleh pada nilai k = 3 dengan learning rate 8 x 10-5. Akurasi model dihitung menggunakan root mean square error (RMSE) dan nilai RMSE model pada eksperimen ini adalah 0,9335.

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Recommendation systems continue to be developed especially in the application of data analysis techniques in helping users on-line find a product (item) that they want to buy. One of several methods in collaborative filtering recommendation system is (CF) approach to latent variable models based on matrix factorization. The relationship between the user and product (item) in the collaborative filtering (CF) can be presented in the form of rating matrix R. This study discusses the collaborative filtering method based on matrix factorization model of recommendation systems.

In the matrix factorization, the main problem is to find two matrices Wmxk and Hk x m so that WH ≈ R with Rmxn. The accuracy of the model is reflected in the norm ║R-WH║ in the testing data. There are several techniques that have been used in the factorization method of collaborative filtering (CF). In this study the method used is matrix factorization with gradient descent methods.

Based on the experiments, the optimal model parameters that meet the optimization function values ​​obtained at k = 3 with a learning rate of 8 x 10-5. The accuracy of the model is calculated using the root mean square error (RMSE) and RMSE values ​​in experimental models is 0.9335."

"Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. "

"This student-friendly introduction to the fundamental concepts and techniques of numerical analysis and numerical methods aims to develop concepts and techniques in a clear, concise, easy-to-read manner, and features fully-worked examples"